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Words starting with algebraicex

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  • algebraic logic functional language — (language)   (ALF) A language by Rudolf Opalla <[email protected]> which combines functional programming and logic programming techniques. ALF is based on Horn clause logic with equality which consists of predicates and Horn clauses for logic programming, and functions and equations for functional programming. Any functional expression can be used in a goal literal and arbitrary predicates can occur in conditions of equations. ALF uses narrowing and rewriting. ALF includes a compiler to Warren Abstract Machine code and run-time support.
  • algebraically — of, occurring in, or utilizing algebra.
  • algebraically closed field — a field in which every polynomial equation with coefficients that are elements of the field has at least one root in the field, as the field of complex numbers.
  • algebraic compiler and translator — (language)   (ACT 1) A language and compiler for the Royal McBee LGP-30, designed around 1959, apparently by Clay S. Boswell, Jr, and programmed by Mel Kaye.
  • algebraic interpretive dialogue — (language)   (AID) A version of Joss II for the PDP-10.
  • algebraic specification language — 1.   (language)   (ASL) 2.   (language)   (ASF) A language for equational specification of abstract data types.
  • algebraic structure — (mathematics)   Any formal mathematical system consisting of a set of objects and operations on those objects. Examples are Boolean algebra, numerical algebra, set algebra and matrix algebra.
  • algebraic data type — (programming)   (Or "sum of products type") In functional programming, new types can be defined, each of which has one or more constructors. Such a type is known as an algebraic data type. E.g. in Haskell we can define a new type, "Tree": data Tree = Empty | Leaf Int | Node Tree Tree with constructors "Empty", "Leaf" and "Node". The constructors can be used much like functions in that they can be (partially) applied to arguments of the appropriate type. For example, the Leaf constructor has the functional type Int -> Tree. A constructor application cannot be reduced (evaluated) like a function application though since it is already in normal form. Functions which operate on algebraic data types can be defined using pattern matching: depth :: Tree -> Int depth Empty = 0 depth (Leaf n) = 1 depth (Node l r) = 1 + max (depth l) (depth r) The most common algebraic data type is the list which has constructors Nil and Cons, written in Haskell using the special syntax "[]" for Nil and infix ":" for Cons. Special cases of algebraic types are product types (only one constructor) and enumeration types (many constructors with no arguments). Algebraic types are one kind of constructed type (i.e. a type formed by combining other types). An algebraic data type may also be an abstract data type (ADT) if it is exported from a module without its constructors. Objects of such a type can only be manipulated using functions defined in the same module as the type itself. In set theory the equivalent of an algebraic data type is a discriminated union - a set whose elements consist of a tag (equivalent to a constructor) and an object of a type corresponding to the tag (equivalent to the constructor arguments).
  • algebraic topology — the branch of mathematics that deals with the application of algebraic methods to topology, especially the study of homology and homotopy.
  • algebraic manipulation package — (mathematics, tool)   (AMP) A symbolic mathematics program written in Modula-2, seen on CompuServe.